This study consists of an elastosonography evaluation of both eyes of 40 glaucomatous patients and 40 healthy subjects. We used shear wave elastography with a one-dimensional-array probe to capture two-dimensional images in order to study the optic nerve near the papilla, chorioretinal complex, lateral rectus muscle, and periorbital fat tissue. Furthermore, we used a two-dimensional array probe to capture three-dimensional images to study the optic nerve in toto with multilevel sampling. We obtained qualitative and quantitative data ("absolute" stiffness values). Then, we have investigated these tissue also measuring the "stiffness ratio" values. Statistically significant differences (p < 0.05), between glaucomatous patients and healthy patients, were noted in "absolute" stiffness values in the two-dimensional analysis at the emergence of the optic nerve and chorioretinal complex, and in the three-dimensional analysis at the emergence of the optic nerve (level I°). This result was supported by the statistically significant differences in the "stiffness ratio" values between the optic nerve and the adjacent adipose tissue, obtained both in two- and three-dimensional analyses. Data were subsequently compared with diagnostic tests currently used for glaucoma, which showed a sensitivity of 83% and specificity of 80% relative to those of elastosonography. We propose the use of elastosonography to verify the existence of pathological changes in the mechanical and elastic properties of peri-ocular structures and their variations as a complementary tool in the diagnosis of glaucoma and for follow-up during treatment.